AUTOMATIC THEOREM-PROVING IN COMBINATORICS ON WORDS

Automatic Theorem-Proving in Combinatorics on Words

We describe a technique for mechanically proving certain kinds of theorems in combinatorics on words, using automata and a package for manipulating them. We illustrate our technique by solving, purely mechanically, an open problem of Currie and Saari on the lengths of unbordered factors in the Thue-Morse sequence. Dedicated to the memory of Sheng Yu (1950–2012): friend and colleague

Automatic Theorem Proving in Walnut

2 Basics 3 2.1 Words and Automata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Number Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Automatic Words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

On the number of Abelian Bordered Words (with an Example of Automatic Theorem-Proving)

In the literature, many bijections between (labeled) Motzkin paths and various other combinatorial objects are studied. We consider abelian (un)bordered words and show the connection with irreducible symmetric Motzkin paths and paths in Z not returning to the origin. This study can be extended to abelian unbordered words over an arbitrary alphabet and we derive expressions to compute the number...

Applied Combinatorics on Words

Combinatorics on Words

Words (strings of symbols) are fundamental in computer processing. Indeed, each bit of data processed by a computer is a string, and nearly all computer software use algorithms on strings. There are also abundant supply of applications of these algorithms in other areas such as data compression, DNA sequence analysis, computer graphics, cryptography, and so on. Combinatorics on words belongs to...